Cabinet ministers today admitted that David Cameron effectively won the first week of the general election campaign with his pledge to halt the National Insurance rise.

Chancellor Alistair Darling conceded after a bruising week of daily arguments over tax and spending cuts: "They may have got the political tactics right for the first day or so."

Another Cabinet minister said: "Yes, they have won the first week — but this is a four-week campaign and we are going to hammer them every day on their failure to say how they will pay for this £30 billion policy. It ain't over yet."

The Conservatives took a risk today by revealing more detail of how they claim they would pay for the NI cut, which shadow chancellor George Osborne says would make Britons £150 a year better off on average.

Sir Peter Gershon, the business chief who advises both the Tories and the Government on efficiency, gave a rare interview in which he said "perhaps £1 billion of £2 billion" in efficiency savings to fund the Tory policy would come from leaving vacancies unfilled.

Experts said that suggested up to 40,000 unfilled posts, a figure which the Conservatives neither confirmed nor denied. Other savings would come from renegotiating major supply contracts and axing consultants.

But Labour said there was still a multi-billion-pound hole in the figures.

Mr Cameron admitted that thousands of jobs would disappear but insisted it would not mean sackings. "If you don't fill all those jobs as they become available, that's one way of saving money relatively rapidly," he said.

He added that Sir Peter's analysis of the savings disproved Gordon Brown's claim that the policy was unfunded.

He also admitted that cutting the deficit would require major spending cuts in addition to efficiency savings.

In response, Mr Darling claimed Mr Cameron had confirmed his intention to make "a very expensive tax cut" but had admitted efficiency savings would not be enough to pay for it.

Lib-Dem Treasury spokesman Vince Cable said: "Claiming that they are the party that will support jobs is entirely undermined when their efficiency chief is looking to immediately slash employment throughout the public sector."